Period-doubling cascades of canards from the extended Bonhoeffer-van der Pol oscillator

This Letter investigates the period-doubling cascades of canards, generated in the extended Bonhoeffer-van der Pol oscillator. Canards appear by Andronov-Hopf bifurcations (AHBs) and it is confirmed that these AHBs are always supercritical in our system. The cascades of period-doubling bifurcation are followed by mixed-mode oscillations. The detailed two-parameter bifurcation diagrams are derived, and it is clarified that the period-doubling bifurcations arise from a narrow parameter value range at which the original canard in the non-extended equation is observed.     

Dynamical pair correlations of classical and quantum fluids perturbed with weak long-range forces

We study time dependent correlation functions of ideal classical and quantum gases using methods of equilibrium statistical mechanics. The basis for this is the path integral formalism of quantum mechanical systems. By this approach the statistical mechanics of a quantum mechanical system becomes the equivalent of a classical polymer problem in four dimensions where imaginary time is the fourth dimension. Several non-trivial results for quantum systems have been obtained earlier by this analogy. Here we will focus upon particle dynamics. First ideal gases are considered. Then interactions, that are assumed weak and of long range, are added, and methods of classical statistical mechanics are applied to obtain the leading contribution. Comparison is performed with known results of kinetic theory. These results demonstrate how methods developed for systems in thermal equilibrium also is applicable outside equilibrium. Thus, more generally, we have reason to expect that these methods will be accurate and useful for other situations of interacting many-body systems consisting of quantized particles too. To indicate so we sketch the computation of the induced Casimir force between parallel plates filled with ions for the situation where the ions are quantized, but the interaction remains electrostatic. Further in this respect we establish expressions for a leading correction to ab initio calculations for the energies of the quantized electrons of molecules. To our knowledge these two latter applications go beyond earlier results.     

Photoreflectance study on the photovoltaic effect in InAs/GaAs quantum dot solar cell

To investigate the effect of quantum dot (QD) layers on the photovoltaic process of InAs/GaAs QD solar cell (QDSC), QD layers were embedded in conventional GaAs p-n junction SC (GaAs SC) structures. The photoreflectance (PR) was examined at different temperatures (T) and excitation light intensities (I_ex) to investigate the photovoltaic effects through observation of the Franz-Keldysh oscillations (FKOs) in the PR spectra. The evaluated the p-n junction electric fields (F_pn) of the InAs QDSC was different from that of the GaAs SC. Moreover, InAs QDSC show that the different photovoltaic behaviors compared with GaAs SC by varying I_ex and T. From these considerations, we suggest that the different photovoltaic behaviors are caused by the effect of the additional photo-carrier generation in InAs QD layers resulting in enhancement of the field screening effect in F_pn.     

Basic properties of nonlinear surface charge waves at a plasma boundary

The nonlinear properties of surface charges are here analyzed under ideal conditions. We thus deduce a new single equation from the wellknown equations which govern the cold electron plasma motion. Simple formulas that describe the propagation of surface charge perturbations along the plasma boundary are also found.     

Numerical Simulation of a Liquid Drop Freely Oscillating

Free oscillations of a viscous liquid drop surrounded by a dynamically inactive ambient gas, in zero gravity, are investigated numerically using FIDAP^TM package in the axisymmetrical case. The full Navier‐Stokes equations with appropriate interfacial conditions are solved by using Galerkin/Finite element technique along with the spine method for the advection of the free boundary are used. The aim of this preliminary study is to demonstrate the ability of the package to accurately solve nonlinear free surface problems. Oscillations of viscous drops released from an initial static deformation of small‐ to large‐amplitude proportional to the second spherical harmonic, without initial internal circulation, are considered. Accuracy is attested by demonstrating that (i) the drop volume remains constant, (ii) dynamic response to small and moderate amplitudes agrees well with linear and weakly non‐linear perturbation theories, (iii) large amplitude oscillations compare well with some numerical and experimental published results.     

Excitation of Forbidden Electronic Transitions in Atoms by Hermite–Gaussian Modes

Photoexcitation of trapped ions by Hermite–Gaussian (HG) modes from guided beam structures is proposed and investigated theoretically. In particular, simple analytical expressions for the matrix elements of induced atomic transitions are derived that depend both on the parameters of HG beams and on the geometry of an experiment. By using these general expressions, the ${}^2{S}_{1/2}\to {}^2{F}_{7/2}$ electric octupole (E3) transition is investigated in an Yb⁺ ion, localized in the low–intensity center of the HG₁₀ and HG₀₁ beams. It is shown how the corresponding Rabi frequency can be enhanced by properly choosing the polarization of incident light and the orientation of an external magnetic field, which defines the quantization axis of a target ion. The calculations, performed for experimentally feasible beam parameters, indicate that the achieved Rabi frequencies can be comparable or even higher than those observed for the conventional Laguerre–Gaussian (LG) modes. Since HG-like modes can be relatively straightforwardly generated with high purity and stability from integrated photonics, these results suggest that they may form a novel tool for investigating highly-forbidden atomic transitions.